Math Problem Statement
Compute the total and annual returns on the described investment. Six years after buying 150 shares of XYZ stock for $60 per share, you sell the stock for $14,400. Question content area bottom Part 1 The total return is enter your response here%. (Do not round until the final answer. Then round to one decimal place as needed.) Part 2 The annual return is . (Do not round until the final answer. Then round to one decimal place as needed.)
Solution
Let's break the problem into two parts: calculating the total return and then the annual return.
Part 1: Total Return
The total return is given by the formula:
Step 1: Initial Value
You bought 150 shares at $60 per share:
Step 2: Final Value
You sold the shares for $14,400, so the Final Value is $14,400.
Step 3: Calculate Total Return
Now, substitute the values into the total return formula:
I'll calculate that next.
Part 2: Annual Return
The annual return can be calculated using the formula for the compound annual growth rate (CAGR):
where:
- (the number of years)
Now let's calculate both the total return and the annual return.### Part 1: Total Return The total return is 60.0%.
Part 2: Annual Return
The annual return is approximately 8.1%.
Would you like any more details or further clarification?
Here are 5 related questions to consider:
- What factors could affect the annual return on investments?
- How does compounding impact the annual return over different periods?
- What is the difference between simple interest and compound interest in long-term investments?
- How does stock price volatility affect potential total returns?
- How can you assess the risk of an investment based on its historical returns?
Tip: Always factor in inflation when assessing the real value of your investment returns over time.
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Math Problem Analysis
Mathematical Concepts
Percentage
Compound Interest
Investment Returns
Formulas
Total Return (%) = ((Final Value - Initial Value) / Initial Value) × 100
Annual Return (%) = ((Final Value / Initial Value)^(1/n) - 1) × 100
Theorems
Compound Annual Growth Rate (CAGR)
Suitable Grade Level
Grades 10-12
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